Non-cooperative games with minmax objectives

We consider noncooperative games where each player minimizes the sum of a smooth function, which depends on the player, and of a possibly nonsmooth function that is the same for all players. For this class of games we consider two approaches: one based on an augmented game that is applicable only to a minmax game and another one derived by a smoothing procedure that is applicable more broadly. In both cases, centralized and, most importantly, distributed algorithms for the computation of Nash equilibria can be derived.